{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# 电子学计算与仿真\n",
    "## 项目一 —— 5种不动点迭代格式计算根号2\n",
    "### 2018级-电子科学与技术专业—董炳飞-20181050117"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### 不动点迭代格式1"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 18,
   "metadata": {
    "scrolled": true
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "1 \t\t 1.0 \t\t -1.0\n",
      "2 \t\t 1.5 \t\t 0.5\n",
      "3 \t\t 1.375 \t\t -0.125\n",
      "4 \t\t 1.4296875 \t\t 0.0546875\n",
      "5 \t\t 1.407684326171875 \t\t -0.022003173828125\n",
      "6 \t\t 1.4168967450968921 \t\t 0.009212418925017118\n",
      "7 \t\t 1.4130985519638084 \t\t -0.003798193133083716\n",
      "8 \t\t 1.4146747931827024 \t\t 0.0015762412188939923\n",
      "9 \t\t 1.4140224079494415 \t\t -0.0006523852332609437\n",
      "10 \t\t 1.4142927228578732 \t\t 0.000270314908431768\n",
      "11 \t\t 1.4141807698935047 \t\t -0.00011195296436850022\n",
      "12 \t\t 1.4142271449252117 \t\t 4.637503170701329e-05\n",
      "13 \t\t 1.4142079362035538 \t\t -1.9208721657948402e-05\n",
      "14 \t\t 1.4142158927929964 \t\t 7.956589442636997e-06\n",
      "15 \t\t 1.4142125970788504 \t\t -3.2957141460343564e-06\n",
      "16 \t\t 1.414213962210597 \t\t 1.365131746533521e-06\n",
      "17 \t\t 1.414213396754899 \t\t -5.654556978207381e-07\n",
      "18 \t\t 1.4142136309743842 \t\t 2.3421948514013025e-07\n",
      "19 \t\t 1.4142135339575084 \t\t -9.701687586627372e-08\n",
      "20 \t\t 1.414213574143216 \t\t 4.018570765040863e-08\n"
     ]
    },
    {
     "data": {
      "text/plain": [
       "Text(3, 1, '$x_n = 1-\\\\frac {(x_{n-1})^2} {2} +(x_{n-1}) $')"
      ]
     },
     "execution_count": 18,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": "iVBORw0KGgoAAAANSUhEUgAAAmsAAAEQCAYAAADvQTN7AAAAOXRFWHRTb2Z0d2FyZQBNYXRwbG90bGliIHZlcnNpb24zLjMuMiwgaHR0cHM6Ly9tYXRwbG90bGliLm9yZy8vihELAAAACXBIWXMAAAsTAAALEwEAmpwYAAA1RElEQVR4nO3dd5hU5fnG8e+zdCyAggoiLBBLRIoKCqKCWCItauQXBYRYEgR7rEQBEaVoNCIKGhIRxRU7FlBs2BUVCCAWEA2IQJQiICL9+f3xzuKwLLuz7O6cmZ37c13nmp1zzszcOx7dx/e8xdwdEREREUlNWVEHEBEREZFdU7EmIiIiksJUrImIiIikMBVrIiIiIilMxZqIiIhICisf1QfXrFnTs7Ozo/p4EZG0NGPGjBXuXivqHCKSPJEVa9nZ2UyfPj2qjxcRSUtmtijqDCKSXLoNKiIiIpLCVKyJiIiIpDAVayIiIiIpTMWaiIiISApTsSYiIiKSwgot1szsIDN708y+MLPPzOzKfM4xMxtpZgvMbI6ZHVU6cUUilpMD2dmQlRUec3KiTiQiImVcIlN3bAGucfeZZrYXMMPMXnP3z+PO6QAcHNuOBe6PPYqUHTk50Ls3rF8fni9aFJ4D9OgRXS4RESnTCm1Zc/dl7j4z9vNPwBfAgXlOOwN4xINpQHUzq13iaUWidNNNrFi/nmuBJbn71q+Hm26KMJSIiJR1ReqzZmbZwJHAR3kOHQgsjnv+HTsXdJhZbzObbmbTly9fXsSoItH5+eefuW3RIhoBdwNvxB/89ttoQomISEZIuFgzsz2BZ4Cr3H1t3sP5vMR32uE+xt1buHuLWrW0Woqkvs2bNzN69GgaNWrEAOAkYA7QK/6kevUiySYiIpkhoWLNzCoQCrUcd382n1O+Aw6Ke14XWFr8eCLR2LZtG48//ji//e1vufTSSznkkEN4f+BAnqtalcbxJ1atCkOGRBVTREQyQCKjQQ14EPjC3f+xi9NeAHrFRoW2Ata4+7ISzCmSNK+99hotW7akW7duVK1alUmTJvH2229z3C23wJgxUKlSOLF+/fBcgwtERKQUJTIatA3QE/jUzGbF9t0I1ANw9weAl4COwAJgPXBBiScVKWXTp0+nX79+vPHGG9SvX59HHnmE7t27U65cuV9P6tED/vWv8PNbb0WSU0REMkuhxZq7v0f+fdLiz3Hg0pIKJZJM8+fPp3///jz11FPUrFmTESNG0KdPHyrltqDl9cc/JjegiIhktERa1kTKpKVLl3LLLbfw4IMPUrlyZQYMGMC1117L3nvvXfALL7kkOQFFRERQsSYZaPXq1dxxxx2MGDGCLVu20LdvX/r378/++++f2BvkTopbtWrphRQREYlRsSYZY8OGDdx3330MHTqUH3/8ke7du3PrrbfSsGHDor1Rx47hUX3WREQkCbSQu5R5W7ZsYezYsRx88MFcd911HHPMMcycOZOcnJyiF2oiIiJJpmJNyix357nnnqNp06ZcdNFF1KlTh6lTpzJlyhSOPPLIqOOJiIgkRMWalEnvvPMObdq04ayzzmLr1q08/fTTTJs2jZNOOinqaCIiIkWiYk3KlDlz5tCpUyfatm3LokWLGDNmDJ999hlnn302YX5nERGR9KIBBlImLFy4kAEDBpCTk0O1atUYPnw4l19+OVVLY8Tm+eeX/HuKiIjsgoo1SWvLly9nyJAhjB49mnLlynHdddfRr18/atSoUXofqmJNRESSSMWapKV169bxj3/8gzvvvJOff/6ZCy+8kJtvvpm6deuW/oevWBEea9Ys/c8SEZGMp2JN0sqmTZsYM2YMt956Kz/88AN/+MMfGDJkCIcddljyQnTtGh41z5qIiCSBijVJC9u2bePxxx9nwIABfPPNN7Rt25bnn3+eVq1aRR1NRESkVGk0qKQ0d2fKlCkcffTR9OjRg7322ouXXnqJN998U4WaiIhkBBVrkrI++ugj2rdvT4cOHVizZg05OTnMnDmTDh06aBoOERHJGCrWJOV8+eWXnH322bRq1YrPPvuMkSNH8uWXX9K9e3eysnTJiohIZlGfNUkZS5YsYdCgQTz00ENUqVKFQYMGcfXVV7PXXntFHW1HfftGnUBERDKIijWJ3I8//sjw4cMZOXIkW7du5dJLL+Wmm25iv/32izpa/s45J+oEIiKSQVSsSWR++eUXRo4cyfDhw1mzZg09evRg8ODBNGjQIOpoBVu8ODwedFC0OUREJCOoWJOk27JlCw899BCDBg1i6dKldOzYkWHDhtG0adOooyWmZ8/wqHnWREQkCdRbW5LG3Xn22Wc54ogj6N27N/Xq1ePtt99m8uTJ6VOoiYiIJJmKNUmK3HnRzj77bLKyspg4cSIffPABJ554YtTRREREUpqKNSlVs2bN4vTTT6d9+/YsWbKEBx98kDlz5nDmmWdqrjQREZEEqFiTUvHNN9/Qo0cPjjzySD7++GPuuOMOvvrqKy688ELKl1dXSRERkUTpr6aUqO+//57bbruNf/7zn5QvX55+/fpxww03UL169aijlZxrrok6gYiIZBAVa1Ii1q5dy1133cVdd93Fhg0buOiii7j55pupU6dO1NFKXpcuUScQEZEMomJNimXjxo088MAD3HbbbaxYsYKuXbty2223ceihh0YdrfTMmxcey/LvKCIiKUPFmuyWrVu38thjjzFw4EAWLlxI+/btGT58OC1btow6Wum7+OLwqHnWREQkCTTAQIrE3Zk8eTJHHnkkvXr1okaNGrzyyiu8/vrrmVGoiYiIJJmKNUnYhx9+SNu2bencuTPr169nwoQJTJ8+ndNOO03TcIiIiJQSFWtSqM8//5wzzzyT4447jvnz5zNq1Cg+//xzzj33XLKydAmJiIiUJv2llV1avHgxF154IU2aNGHq1KnceuutLFiwgEsuuYSKFStGHU9ERCQjaICB7GTlypUMGzaM++67D3fnyiuv5MYbb6RmzZpRR0sN/ftHnUBERDKIijXZbv369dxzzz3cfvvtrF27lp49ezJ48GDq168fdbTUcsopUScQEZEMomJN2Lx5M2PHjuWWW25h2bJldO7cmaFDh9KkSZOoo6WmWbPCY/PmUaYQEZEMUWifNTMba2Y/mNncXRxvZ2ZrzGxWbBtY8jFjcnIgOxuyssJjTk6pfVSZFfcdev36PHXFFTRu3Jg+ffrQoEED3n33XV588UUVagW56qqwiYiIJEEiLWvjgPuARwo4511371wiiXYlJwd694b168PzRYvCc4AePUr1o8uMuO/wDaDft98y/d57aVy3Ls8//zxdunTRFBwiIiIpptBizd3fMbPsJGQp2E03wfr1fExLRnEpFdlEpfUbqdR3PZWGvUCldSuplLWZSlmbqGhbqHTwQVTqdjaVKkGlu4dT6edVVLJNVMzaQpWsjezbrgm1br2CqlWBDh3gl192/LzOneHaa8PP7drtnOePf4RLLgnFY8eOOx8///ywrVgBXbvufLxvXzjnHFi8GHr23Pn4NdeENSjnzft1xvx4/fuHvlOzZuXfyjN0KBx3HHzwAdx4Y9g3bRqXbtzI6NgpBwEPAT2zsij3+9/v/B4iIiISuZLqs9bazGYDS4Fr3f2z/E4ys95Ab4B69eoV7RO+/RaA5dTibdqykUpspBKbfqrIxs8rs8Xz/CoLgJdzn/Tb+f1mAv+AqlWh5rZx1Cq/mpoV1lCrwmpqVVhNzTdqU6sa1KwJtdY0CfsqrKFG+Z/IMi9a9hQwaskSLtu4cfvz64FbgMoQCkYRERFJSeZeeOERa1mb5O5H5HNsb2Cbu68zs47APe5+cGHv2aJFC58+fXriSbOzw63PvOrXh4UL2boVNm2CjRt/3fI+z93Wr4dVq2D58tDwtXz5jj+vWAHr1uUfo1y5UMBlZ0OjRtCw4a9bo0ZQp07oUpcqpkyZQocOHXbY9ymwwz/I2HcoCcptadXaoBIBM5vh7i2iziEiyVPsljV3Xxv380tmNtrMarr7iuK+9w6GDNmxzxqEZrEhQ4BQRFWpEraSsGHDjsVb/OP//hdqmw8/hCeegK1bf31dxYrQoMGvxVt8MdewIeyxR8nkK8xnn33GEUfsWFu/dN11dBg1apffoSRo6NCoE4iISAYpdrFmZgcA37u7m9kxhBGmK4udLK/cQQR9+oRmr/r1Q5FRSoMLKleGunXDVpDNm8NdxK+/hm+++XX7+mt4/31Yu3bH8/ffPxRxTZuGmR+aN4cmTULNtJOcnNBX79tvoV69/H/fPOf8cP317H/ppTuccu+993LZZZeFJ82awUUXhSbGUv4Oy6zjjos6gYiIZJBCb4Oa2QSgHVAT+B64GagA4O4PmNllQF9gC/ALcLW7f1DYBxf5Nmgacocff9y5kJs/H+bMgdWrw3lZWXDIIb8Wb82bQ/Ovn2H/63rt3Ao2Zkz4+bzzdvisDUDeRsU+ffpw//337xxMt/GK54PY5a2iTSKg26AimSehPmulIROKtYK4hy54s2aFbfbs8BjfdewAltGcWTRjNs2ZRXNmcfA+qyi3avn2c7YB5fK8d4uKFfkkbjDBTlSsFY++P4mQijWRzJN+Kxjkzq2W28KUpszCIIXsbDjzzF/3//hjaHWb1e4qZtGMWTTnDU5mM2Hh9Cqr1tOM2bThfe7iXeA9YNX2128Gym/alLxfREREREpV+hVr8+dHnaBU1agBbdtC2/rPwaJ7ANhEBb7gt7G2teaMpwXTuAyIzQPHp5zPu/yOd/iedzmw3PdRxRcREZESlkKTTMgOhgwJQ0uBimymGXNYWi6HEVzNSk4EqgMn0JKb+B1LeJqedONx6rKERlvnccEF8NBDsGBBuOW6XU4OfPUVvPOOluwSERFJA+nXspZJYlXWC8AZsMMcIZPZSEfeI9wGhS2UYxbNeZcTeKfK6bz4YiPGjQvn1q4NJ54IJ1T+hBOfuIfGG5aRhWvJLhERkTSQfgMMMqVzd3Y2PyxaxP55dt9hxnUF/TOLDS3dNnAQXzY7h3eeW8W798zg7dXNWbKpFgD7sJLTeJVOTKYDL7Nv/b00KW5RzJoVHps3jzKFZCgNMBDJPOnXspYBfyDXr1/PsYsWMTdu3znA4xBa2w47LMwBkncgQaVKYUbe/fcnKwsOPxwO3+tn+rw6BHdY+M4i3uUEptKel+nA43Qji620WjSNzsOgU6cw55vWci9EBlyDIiKSOtKvZa0M27p1K127duW5557bvu9O4Jr4k4qzNFTckl3bMGZwNJPozOSKZzFjU1MADjooFG2dOkH79ruYrDfTvf56eDzllGhzSEZSy5pI5tEAgxTg7lx33XWUL19+e6F2ySmnsK1KlR0LteIuDTVkyPbqKwunJdO5peodTB/7KUuXwr//DS1awPjx0KUL7LtvKNpGj85/WdaMddttYRMREUmC9CvWzjtvp9n709kDDzxAVlYWd955JwCnnXYamzZtYtRrr2H/+ldoSTMLj2PGFG8gQI8e4T3yec/atcMqVM8+CytXwquvwsUXw7x5cOmloVGuSRPo1w/eew+2bSuZ319EREQKln63QcvIAINJkybRpUuX7c8bNmzIf/7zH/bee+8IU+3MPUxtN2kSTJ4M774LW7ZAnTpwzjnQrVtojcuofm5l5BqU9KTboCKZJ/1a1tLcjBkzMLMdCrXFixfz9ddfp1yhBqEIO/RQuOYamDoVVqyAxx4LBdp998Exx4R1TQcMgM8/jzqtiIhI2aNiLUkWLVqEmdGixa//Qzx79mzcnbp160aYrGiqVQutac8/D99/H/q51a8PQ4dC48bQrBkMH66ZQEREUokZB5nxmhmfm/GpGf8yi61jKClPxVopW716NbVr1yY7O3v7vldffRV3p2nTptEFKwE1aoR+bq+/DkuWwD33hPELf/tbmEGkTZvQ+vZ9WVv96p//DJuIZBwzHjdjZNQ5CmLGIDNezbN7C3CjO4cDzYA9gSuSHk52S/oVa61bhy3Fbdy4kRNOOIEaNWrwv//9D4CxY8fi7px66qkRpyt5BxwAV1wBH34YpoAbOhR++gkuvzz0bzvttLD81erVUSctAYceGjYRyShmNAPOAv4edZZCjARam3FS7g53lrnzSeznbcB0IDuaeFJU6TfAIMW5OxdeeCHjctd6AgYMGMDgwYOjCxWhuXNhwgR4/PFQxFWsCB07woUXhsdy5aJOuBtefDE8xvU7FEkWDTCIjhkPATXdSfl/+c14BNjbnTPzOVYZ+AS4zp0pyc4mRZd+LWspbMiQIWRlZW0v1Lp3787WrVsztlADOOKIML3bggUwbRr07Rta337/+zAdyC23wHffRZ2yiO66K2wikjHM2AP4P+DJPPuPNsPN+FPcvr3MmG3Gu2ZUSnbWmKeATmbUjN9pRjlgPDBVhVr6SL9i7eyzw5ZCcnJyMDP69+8PwDHHHMMvv/xCTk4OWVnp9xWXBjM49lgYMQIWL4annw7LYQ0aFAYonHEGvPTSDmvVi4ikktbAHsD78TvdmQFMBPqbUc6M8oRCqRJwhjsbk540eI+wpGS73B1mGDAW+AW4KpJUslvSr5JYuTJsKeCtt97CzDgvNknvPvvsw4oVK/joo4+oXLlyxOlSV4UKod5+5RX4+mu4/vrQ6tapEzRsCLfeCkuXRp1SRGQHLYF17nyTz7GBQEPgPGAUcCTQ0Z1VScy3A3d+BL4Fjo3bPZowsOACd6LpAyW7Jf2KtRTw+eefY2acdNL2vpssWLCAlStXsu+++0aYLP00bAjDhoXWtqeeCnO2DRwI9erBWWfBlClqbRORlFAbWJHfAXfmAk8QiqHzgM67KOqSbQUhN2a0AfoAhwEzzJhlxt1RhpPEqVgrgmXLllGuXDkaN268fd+0adNwdxo1ahRhsvRXsSJ07QqvvQZffRUm4X3/fejQARo1Cv3eli2LOqWIZLDKUOAtza+AqsB9uaMuS5MZQ834b6y/3G92cdoGoAqAO++7Y+40dqd5bPtraeeUkqFiLQHr1q3j0EMPpU6dOmyLLYo5ceJE3J1jjz22kFdLUf3mN3D77WHgwRNPhGKtf//Q2pZ7+zTStUnHjw+biGSSVUD1/A6YcQ5wE2GEZU+zUCCVsknAicCiAs6pAaRGvyEplvQr1k4+OWxJsGXLFrp06cJee+3F/PnzARgxYgTuzplnnpmUDJmsYkX44x/hjTfC+qR//Su88w6cfnoYZTp2LGyMouvuQQeFTURKjBmHmnGlGY+a8aUZ22KtRl2jzhYzD6gVGxW6nRknAA8DNwBdgX2BS/K+2IxRZtxtxmQzlpjxYHHCuPOBO4t3ddyMLKBeLHdaMKNV7J/78KizlCYzqpqxzIxPYoM+CpV+xdqAAWErRe7OX//6VypUqMCkSZMAuOKKK9i2bRtXXnllqX625O/gg+GOO0Jr2/jxoZC76KIw/cewYfDjj0kM88QTYRORktQXGAH0AA6FxP6IJdH7hL+ZR+XuMOMw4HngQXfucudbYBxwgxl75nl9c0JL15lAI+APZpTmgtCHE0avvluKn1FiYkXLSGAtcHvEcUqVO+uBIUALoFcir0m/Yq2U3XvvvWRlZTFixAgAOnbsyObNm7nnnnswS7X/dmSeSpXgvPPgP/8J/duaNYMbbwwNXVddlaQ1Se+/P2wiUpLmElYGOAf4DfB2tHF25M58YA7QEcCM/YGXgQ/YcdmmIUC1+H2xVq4mwA3ubAY2E4rRn+M/w4wPzfhfPtvu9IHrSLhFWur950pIN8KI25Gxkaxl3Rjgf8DQRNZoTb9irUOHsJWw559/HjPjiivCv1+HHHIIP/30E5MnT6Z8+fIl/nlSPGZwyilhtOjs2fCHP8CoUaG/W7duMHNm1AlFpCjc+bc717vzpDtfR51nF/4FnGtGljvfu9PAnc7ubB+z7s637lRyZ2jc6w4GlrqTu1LyYcCC+NfFXtvanQPy2VruRtZuwNjSnqLDjHGx29XZxXyrqwAnzANX5rmzCXgUqEOYbLlA6Ves/fJL2ErIxx9/jJlt74OWlZXF0qVLmTdvHnvumbcVW1JR06bwyCPw3/+Gfm2TJ8PRR0P79vDyyxDRimoiSREbFehmvJbPMTMjJ3b8JTMqRJGxDPk3YaLZPxTxdc0Ja3HmOgootf+lNKM9UB9Se8H5XGa0JLSqve3Owl2cUxav84djjzv1ccwr/Yq1EvLNN99gZjuM5pw7dy5bt26ldu3aESaT3VW3Lvz972HOtr//PQxK6NgRmjSBceMiGowgUvqGAT8Ap5hxSp5j9wLdCf2Wzo7dgpPd5M4G4HxCwVYURwIz4p4Xu1gz4w4zvgPqAu+a8WHc4T2BXu6sLs5nJNGZscfXCzinzF3nsfn5vgdam1GroHMzrlhbtWoV++677w7zok2dOhV332H+NElf1arBtdeGheMfeSQsFn/BBdCgQZgSZPXqqBOKlBx3fgJuiT0dlrvfjMHApYQiobM7JXJLIu62V1G37JL4/Ki584Y7jxfxNf3cf52A1p2/uvNAMXNc705dd8q7U9ud1nHHXnBnUnHeP8naxR4/3NUJyb7Ok+hDQv/Fkwo6KWM6Y23YsIG2bdvy8ccfb9/38MMP06tXQgMxJA1VrAg9e4YBCa+9BnfeCf36wW23weWXh4l3d2vBiaefLvGsIsU0BrgcaBGb6uJAYADwBXC6O2tL8LPe283XrSvBDFK2NI89flHIecm8zoskNjHxtUAr4AjgS3eOSOClnxNaFo8EntzVSelXrHXuXKTTt23bRs+ePXnssce27xs8eDADSnn6D0kdZnDaaWGbNQuGDw/bffeFEaRXXw3VqxfhDWvWLJ2gIrvJnS1m3ECYRuJ+wlxfC4FT3fNfIqkYn/VvQt+tlGXGHcDvd+OlJ7uzpKTzlAVm/Bk4Pp9DufvuNMu3IL+2oGswNm9d1djTAifwTeZ1vhsaA52Ajwh3LRO9c5m7fuz+BZ7l7pFsRx99tJe2gQMHOmF0iQN+/vnn+7Zt20r9cyX1ffqpe9eu7uBerZr74MHua9Yk+OKHHgqbSASA6b6L/66Czw1Davx78Ea7Oi8dNvC3Yr9L19147aOx1xZ1y476907VDXxcaXyn4HVi520oQpaUu87Bs/J8V3MTfN1fYr/LswWdl34tawkYN24cF1xwwfbnbdq04Y033qBSpUoRppJUcsQRYeH42bNh0KCwePzdd8N114VbpAUOBB43Ljyef37pBxVJkBlXEP7vHsI6lru8JWTGcsIEtBsIk9HWJsxr1tO94NaNAlpYClNgC0tJcuc8woLqJcKsdKe/SBXuu56I2J3zCYMrdmDGOOBPQAPfxUjOQqyOPVYyo5J7geuvJu06Lyp3dncRxNyJkQucWy79irV27cLjW2/tdOj111/n1FNP3f58v/3248svv6RGjRrJySZpp1kzmDgRZsyAm28OE+z+4x9w/fVwySWwxx6Fv4dI1Mz4E+GP0hLCKMMuwM3AZfmcWweoCVwETCX0AToQuA+4DuhXyMcdT/jjXFSDIPJbVbuloCJGised9Wb8TFhtYR9g2a7OTfJ1niy5Pad/KOikMjEadM6cOZjZDoXaf//7X77//nsVapKQo4+GSZNg2rTw8/XXQ8OGobWtBKf1EylxZpwFPEjo+3IqYWTcBuBiMw7J5yVNY49PuPNnd1720A9tKuR7/g7cOd8d241tYYn8wmWQGf9nxnNmfGfGz2bMNuPPia4bWQbkTmNy+K5OSPZ1nkS5v3OBU7kUWqyZ2Vgz+8HM5u7iuJnZSDNbYGZzzOyo/M4rETk54a/p229DdjZL7r0XM6NZs2bbT/nkk09wd7Kzs0sthpRdxx4bVkV4770wP9vVV0OjRmEwwoYN7HQNkpMTdWTJYLH5piYA6wmj4b7wsLj3fYQ7J/ktiN0U2JTPsX2A5aUYV3btauAX4BpCa9FLwD8JrZGZ4M3YY+v8DibjOjejmhmHJbBVzfvaYmpF6Ff/VoFnFd75jRMJE/jl21mOsP7Yy4R5QloBHyXSqa7IAwwefdS9alV38LXgDeMGDgD+wgsvFO39RBLw1lvuJ5zgDu5191nn91e43DdSwbf3nq1aNVybIklCbIABeCvwdeAbwE/yHTst7wO+OnaZHp/n2KPg7+XZZ+A/gV/uCfz3uzQ28KPAp8Vta2P558fvjypfKf/uNfPZNwZ8TXzH9VTc4gYeZBfjPY6Mvcdb+RxLynUOfn6CAyZOSfA7KXSAAXiT2Hu+X9i5hfZZc/d3zCy7gFPOAB7x8MnTzKy6mdV2913ed94tN90E69czEzg6bveo8uW5pE0buOuusEHo+H3++bBiBXTtuvN79e0L55wTprrv2XPn49dcA126wLx5cPHFOx/v3z8sTDlrVpj7Ia+hQ+G44+CDD0InqLxGjIDmzeH118OkX3n9859w6KHw4ou//k7xxo8PK5c/8UT+C4o//XSYXmLcuF87w8d76SWoWhVGj4Yn85nWJbc/4J13hnuD8apUCWs4Adx6K7zxxo7H990Xnnkm/Py3v8GHeeY4rFsXHn00/HzVVeE7jHfIITBmTPi5d++wDEG85s3D9wdhArXvvtvxeOvWMCw2X+LZZ8PKPH1ITz4Zcqdt6dBh53ucnTuHGXUB2rWjLfC2wdSmRzHg0/+jr49kOFdzG/3pzmNkrV8frs0ePRBJFjOaEFpfKgFd3be3TADgziozbgeGAncS/kc6VzN2XiT9N4RZ72eXWujC7Q0cm8/+g5MdJNk8/4EX/wH+QuhEvz65iZLLnf+YMQ040Yxsj90yT+Z17s44YFxJ/D5FkNv3c3RhJ5ZEn7UDgcVxz7+L7duJmfU2s+lmNn358iK2tn/7bXiP2NNrgW3AJVu2FDGuSNGYwck1ZvK+H8fLnM6+rKQnj3IsH/Eux2+/NkWSxZ1P3dnHnQruPL+Lc4Z56Cu2/Q+YGRWBQ4FZeU5vHnuMrFhz5y1PoO9bVPkicAKw0D21CzX/tQ/jwmK+1T2EP/EXxr13mbvOc8Uy9gCWAk8Ven5oECvsTS0bmOTuO83Ga2aTgWHu/l7s+RvA9e4+I++58Vq0aOHTp08v6JQdZWfDokU7769fHxYuTPx9RHZX7BrchpFDD/7GMJZQl7OrvsTtczoSt4KZSKkxsxnu3mL3Xkszwh+wlu6/LixuxhCguzsNSialFIcZxxNahW5w586o8yRDbDDFNELn/4buBU9lUch7Jf06j/Vl6xh7einQiNAXEeATdxblOf8ywpqm57tvX9B9l0qiZe074KC453UJlWLJGjIk3LqLV7Vq2C+SDLFrMAunJ48yn0MYXGEwU7aeym9/G+6e/7jb/3kRSYqmwBYg74Cx3D9uEjEz6gJPEIq1uws5vcxwx4ErgGrADcV8uyiu8/0ILWRPEdY6PSju+Q7rfsYKu5uA6cAjibx5SRRrLwC9YqNCWwFrSry/GoQ+QWPGhJY0s/A4Zoz6Ckny5LkGq9bfjwEPNeKr/1agV68wzcdvfgP33gubN0cdVmRn7oyP3VLakGd/Z3fOiiqXBGZUJwzYWwWc5c7WaBMllzsfuZPlXrw50KK4zt1ZWMDt+3F5zl3vTm13WsaK1EIVehvUzCYQqsSawPeECegqhA/0B8zMCMNnTyd0grzA3Qu9v1nk26AiKW7WrNC6NnVqGB/y97+H8QqWSb1spNQV5zaopC4zqgCvAfWA1q41SiVOQn3WSoOKNSmL3GHy5DCgdN48aN8+DOht3jzqZFJWqFgre8woD0wEjgNOcOfziCNJiikTKxiIpAqz0Jr26afhdujs2XDUUXDRRbC05HtyikjZMBroDAwB9jajVdy2dyGvlQygYk2kFFSoAJddBgsWhFuj48eHKeRuvRXWp/RAfBGJwGmxx7uAD/NspbcqkKQNFWsipah69dB37Ysvwhy8AweGou2JJ8ItUxERd7IL6Jz+VtT5JHoq1kSSoFEjeOopePdd2H9/OPdcOP300PImIiJSEBVrIkl0/PHw8cehP9u0aXDEETB4MGzcGHUyERFJVSrWRJKsXLnQn+3LL+Gss+Dmm6Fp052XWRUREQEVayKRqV0bJkyAV16BrVvhlFPCvLv/+1/UyUREJJWoWBOJ2Gmnwdy5oYXt6afhsMNg9OhQwImIiKhYE0kBlSvDoEFhfraWLeHSS6F1a5g5M+pkIiISNRVrIinkkEPg1Vfhscfg229D4XbllbB2bdTJREQkKirWRFKMGXTrFgYg9OkTRo4edhg8+aTmZhMRyUQq1kRSVPXqMGoUfPRRGIxwzjlhYt2vv446mYiIJJOKNZEU17JlmJtt5Ej44ANo3Bhuvx22bIk6mYiIJIOKNZE0UK4cXH55uDXaqRP06wdt2oRlrEREpGxTsSaSRurUCdN7TJgQlqo68siw9qim+RARKbtUrImkGbOwtujnn0PHjnD99WEZq3nzok4mIiKlQcWaSJraf3945hnIyYH586F5c7jrLrWyiYiUNSrWRNKYGXTvDp99Br/7HVx7LZx4YijeRESkbFCxJlIGHHAATJwI48eHQQfNmsHdd6uVTUSkLFCxJlJGmMF554VWtlNPhauvhrZt4auvok4mIiLFoWJNpIypXRuefx4efjgUbs2awT33wLZtUScTEZHdoWJNpAwyg169QrHWvj1cdRW0axem+xARkfSiYk2kDKtTB158EcaNgzlzQivbvfeqlU1EJJ2oWBMp48zgT38KrWxt28IVV8Dpp8OyZVEnExGRRKhYE8kQBx4IkyfDmDHw3nvQtGl4LiIiqU3FmkgGMYO//AVmzAjFW+fOoaVtw4aok4mIyK6oWBPJQL/9LUybBldeGfqwHXusFoUXEUlVKtZEMlTlyjBiRLgVumwZHH10uEXqHnUyERGJp2JNJMN17BhGih5/PFx8MXTtCqtWRZ1KRERyqVgTEQ44AKZMgb//PUz10awZvP121KlERARUrIlITFZWWAj+ww+hSpUwme7AgbBlS9TJREQym4o1EdnB0UfDzJlhbrZbbw1zsy1cGHUqEZHMpWJNRHay554wdixMmABz50Lz5vDEE1GnEhHJTCrWRGSXzj0XZs2Cww8PP19wAaxbF3UqEZHMklCxZmanm9k8M1tgZv3yOd7OzNaY2azYNrDko4pIFBo0gHfegf794eGH4aijQgEnIiLJUWixZmblgFFAB+BwoJuZHZ7Pqe+6e/PYNriEc4pIhMqXD/3X3nwT1q+H1q3hoYeiTiUikhkSaVk7Bljg7t+4+ybgceCM0o0lIqmobVv4z3/guOPgwguhd28tVSUiUtoSKdYOBBbHPf8uti+v1mY228xeNrPG+b2RmfU2s+lmNn358uW7EVdEolarFrz6Kvztb/Cvf4XJdDVaVESk9CRSrFk++/IuSDMTqO/uzYB7gefyeyN3H+PuLdy9Ra1atYoUVERSR7lyMHQoPPccLFgQpvuYMiXqVCIiZVMixdp3wEFxz+sCS+NPcPe17r4u9vNLQAUzq1liKUUkJZ1xBkyfDnXrhmWrbrkFtm2LOpWISNmSSLH2CXCwmTUws4rAucAL8SeY2QFmZrGfj4m978qSDisiqec3vwmrHpx3HgwaBJ06aW1REZGSVGix5u5bgMuAV4AvgCfd/TMz62NmfWKndQXmmtlsYCRwrrvnvVUqImVU1aphWo/774epU8P0HjNmRJ1KRKRssKhqqhYtWvj06dMj+WwRKT0ffwxdu8IPP8B998Gf/xx1orLFzGa4e4uoc4hI8mgFAxEpUcccE9YWPfFE+Mtf4KKL4Jdfok4lIpK+VKyJSImrWRNefjmsejB2LLRpA998E3UqEZH0pGJNREpFuXJh1YMXX4T//jdM7zFpUtSpRETSj4o1ESlVnTuHwQbZ2dClCwwYAFu3Rp1KRCR9qFgTkVLXsCF88AFccAHcdhv8/vewdm3UqURE0oOKNRFJiipV4MEHYfRoeOWVsBj8119HnUpEJPWpWBORpDGDvn3D2qLLloWRo2+9FXUqEZHUpmJNRJKuffswH9t++8Gpp4YF4UVEJH8q1kQkErnLVJ18MvTuDVdeCVu2RJ1KRCT1qFgTkchUrx6m87jqKhg5Mqwrunp1xKFERFKMijURiVT58nD33eFW6JtvQqtWMH9+1KlERFKHijURSQl//jO8/jqsXAnHHht+FhERFWsikkJOPDEMPDjwQDj9dBg1KupEIiLRU7EmIimlQYMwgW6HDnDZZXDJJbB5c9SpRESio2JNRFLO3nvDc8/B9dfD/feHVrZVq6JOJSISDRVrIpKSypWD22+Hhx+G994LE+h+8UXUqUREkk/FmoiktF69wijRn34KI0WnTIk6kYhIcqlYE5GUd9xx8MknoT9bp05w331RJxIRSR4VayKSFurVC7dDu3SByy+HG26AbduiTiUiUvpUrIlI2thzT3jmmTBC9I474LzzYOPGqFOJiJSu8lEHEBEpinLlwm3QevWgXz9YtgwmTgxLV4mIlEVqWRORtGMWboM++ii8/z4cfzwsXhx1KhGR0qFiTUTSVo8eYXTo4sVhpOicOVEnEhEpeSrWRCSttW8fBh6YhRa2N96IOpGISMlSsSYiaa9JE5g2DerXD6sdjB8fdSIRkZKjYk1EyoS6dUML2wknhIl0hw0D96hTiYgUn4o1ESkzqlWDl1+G7t3hxhvDFB9btkSdSkSkeDR1h4iUKZUqhdug9erB8OGwZAlMmAB77BF1MhGR3aOWNREpc7Kywm3QUaNg8uQwCOGHH6JOJSKye1SsiUiZdckl8Oyz8OmnYX3RBQuiTiQiUnQq1kSkTDvjDJg6FVavhtat4aOPok4kIlI0KtZEpMxr1Qo++AD23htOOgkmTYo6kYhI4lSsiUhGOOQQ+PBDOPxwOOusMOhARCQdqFgTkYyx337hlmibNmGpqgceiDqRiEjhEirWzOx0M5tnZgvMrF8+x83MRsaOzzGzo0o+qohI8e29d5iLrVMn6Ns3TO8hIpLKCi3WzKwcMAroABwOdDOzw/Oc1gE4OLb1Bu4v4ZwiIiWmSpUwSrRbN/jb36BfP612ICKpK5FJcY8BFrj7NwBm9jhwBvB53DlnAI+4uwPTzKy6mdV292UlnlhEpARUqBAmz61WDW6/HdasCfOyZalziIikmESKtQOBxXHPvwOOTeCcA4EdijUz601oeaNevXpFzSoiUqLKlYPRo6F69XA7dO1aGDcuFHIiIqkikWLN8tmX94ZBIufg7mOAMQAtWrTQTQcRiZxZWO2gWrVwS3TtWnjyyXCrVEQkFSTS4P8dcFDc87rA0t04R0QkZfXrB/ffH5an6tAhFG0iIqkgkWLtE+BgM2tgZhWBc4EX8pzzAtArNiq0FbBG/dVEJN306QM5OfD++3DyybBiRdSJREQSKNbcfQtwGfAK8AXwpLt/ZmZ9zKxP7LSXgG+ABcC/gEtKKa+ISKnq1g0mToS5c6FtW1iyJOpEIpLpzCMar96iRQufPn16JJ8tIlKYt96CLl2gVi14/XVo2DDqRIGZzXD3FlHnEJHk0SB1EZF8tGsXVjtYswaOPz60tImIREHFmojILrRsCe+8E0aMtm0LH38cdSIRyUQq1kRECtC4Mbz3XpiL7eST4c03o04kIplGxZqISCEaNAgFW/36YVqPSZOiTiQimUTFmohIAmrXhrffhqZN4Q9/gBfyTmAkIlJKVKyJiCRo333htdfgqKOga1d47rmoE4lIJlCxJiJSBNWqwSuvwNFHw//9Hzz7bNSJRKSsU7EmIlJEuQXbMcfAH/8ITz8ddSIRKctUrImI7Ia994YpU6BVKzj3XHjiiagTiUhZpWJNRGQ37bUXvPwyHHccdO8OEyZEnUhEyiIVayIixbDXXvDSS3DCCXDeeWEheBGRkqRiTUSkmPbcEyZPDqsc9OoF48dHnUhEyhIVayIiJWCPPcJkue3awZ/+BA8/HHUiESkrVKyJiJSQqlXhxRfDslQXXAAPPRR1IhEpC1SsiYiUoKpVw+oGp54KF10EDz4YdSIRSXcq1kRESliVKvD88/C738Gf/wxjxkSdSETSmYo1EZFSULkyTJwIHTvCxRfDAw9EnUhE0pWKNRGRUlK5cliOqlMn6NsXRo2KOpGIpCMVayIipahSJXjmGejSBS67DO69N+pEIpJuVKyJiJSySpXC+qFnnAFXXKGCTUSKRsWaiEgSVKwITz4J3bpBo0ZRpxGRdFI+6gAiIpmiYkV47LGoU4hIulHLmoiIiEgKU7EmIiIiksJUrImIiIikMBVrIiIiIilMxZqIiIhIClOxJiIiIpLCVKyJiIiIpDAVayIiIiIpzNw9mg82Ww4s2s2X1wRWlGCckpbq+SD1Mypf8Shf8aRyvvruXivqECKSPJEVa8VhZtPdvUXUOXYl1fNB6mdUvuJRvuJJ9Xwikll0G1REREQkhalYExEREUlh6VqsjYk6QCFSPR+kfkblKx7lK55UzyciGSQt+6yJiIiIZIp0bVkTERERyQgq1kRERERSWEoVa2Y21sx+MLO5uzhuZjbSzBaY2RwzOyru2OlmNi92rF9E+XrEcs0xsw/MrFncsYVm9qmZzTKz6RHla2dma2IZZpnZwLhjqfD9XReXba6ZbTWzfWLHkvH9HWRmb5rZF2b2mZldmc85kV2DCeaL7BpMMF9k12CC+SK9BkVE8uXuKbMBJwJHAXN3cbwj8DJgQCvgo9j+csDXQEOgIjAbODyCfMcBNWI/d8jNF3u+EKgZ8ffXDpiUz/6U+P7ynNsFmJrk7682cFTs572A+Xm/hyivwQTzRXYNJpgvsmswkXxRX4PatGnTlt+WUi1r7v4OsKqAU84AHvFgGlDdzGoDxwAL3P0bd98EPB47N6n53P0Dd/8x9nQaULekMxQkge9vV1Li+8ujGzChpDMUxN2XufvM2M8/AV8AB+Y5LbJrMJF8UV6DCX5/u5IS318eSb8GRUTyk1LFWgIOBBbHPf8utm9X+6N0EaEFJpcDr5rZDDPrHVEmgNZmNtvMXjazxrF9KfX9mVlV4HTgmbjdSf3+zCwbOBL4KM+hlLgGC8gXL7JrsJB8kV+DhX1/qXANiojkKh91gCKyfPZ5AfsjYWYnEf5QHh+3u427LzWz/YDXzOzLWEtTMs0krCu4zsw6As8BB5Ni3x/h9tP77h7fCpe078/M9iT8kb7K3dfmPZzPS5J6DRaSL/ecyK7BQvJFfg0m8v0R8TUoIhIv3VrWvgMOinteF1hawP6kM7OmwL+BM9x9Ze5+d18ae/wBmEi47ZNU7r7W3dfFfn4JqGBmNUmh7y/mXPLcfkrW92dmFQh/yHPc/dl8Ton0GkwgX6TXYGH5or4GE/n+YiK7BkVE8kq3Yu0FoFdsRF4rYI27LwM+AQ42swZmVpHwH9oXkh3OzOoBzwI93X1+3P49zGyv3J+B04B8R0SWcr4DzMxiPx9D+Oe/khT5/mK5qgFtgefj9iXl+4t9Nw8CX7j7P3ZxWmTXYCL5orwGE8wX2TWY4D/fSK9BEZH8pNRtUDObQBgtVtPMvgNuBioAuPsDwEuE0XgLgPXABbFjW8zsMuAVwqiyse7+WQT5BgL7AqNjf4+2uHsLYH9gYmxfeeAxd58SQb6uQF8z2wL8Apzr7g6kyvcHcBbwqrv/HPfSpHx/QBugJ/Cpmc2K7bsRqBeXMcprMJF8UV6DieSL8hpMJB9Eew2KiOxEy02JiIiIpLB0uw0qIiIiklFUrImIiIikMBVrIiIiIilMxZqIiIhIClOxJiIiIpLCVKyJiIiIpDAVayIiIiIpTMWaiIiISApTsSYiIiKSwlSsScYzs3+amZvZlNx1K/McHxc7/mJ+x0VEREqTlpuSjGdmlYFpQDPgRncfFnfsT8A4YDHQ3N1XRRJSREQyloo1EcDMDgFmAJWBdu7+vpn9FpgOVMzdF2VGERHJTLoNKgK4+3zgYqA88LiZHQQ8BVQF+qtQExGRqKhlTSSOmY0B/gKsAaoBU4COrn9RREQkIirWROLE+q99CdQHfgAau/uKaFOJiEgm021QkR2dCNSL/bwPcHCEWURERFSsieQys9rAeMCAh/i1/1qNSIOJiEhGU7EmAphZFpAD7Afc4+4XAo8QWtkeijKbiIhkNhVrIsFA4CTCVB3Xx/ZdQui/doaZXRlVMBERyWwaYCAZz8xOAl4H1gFHufvXcceaAB8T/semjbtPjyaliIhkKrWsSUYzs/0Itz+zgL/EF2oA7v4pcBVhYtwnzKxa0kOKiEhGU8uaiIiISApTy5qIiIhIClOxJiIiIpLCVKyJiIiIpDAVayIiIiIpTMWaiIiISApTsSYiIiKSwlSsiYiIiKQwFWsiIiIiKUzFmoiIiEgK+3/UmRiQERQmkQAAAABJRU5ErkJggg==\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "import matplotlib.pyplot as plt\n",
    "import numpy as np\n",
    "%matplotlib inline\n",
    "def squareTwo(old):\n",
    "    return 1-((old**2)/2)+old\n",
    "\n",
    "old = 2\n",
    "new = 0\n",
    "x = []\n",
    "y = []\n",
    "for val in range(20):\n",
    "    x.append(old)\n",
    "    new = squareTwo(old)\n",
    "    y.append(old)\n",
    "    x.append(old)\n",
    "    y.append(new)\n",
    "    \n",
    "    print(val + 1, \"\\t\\t\", new, \"\\t\\t\", new - old)\n",
    "    old = new\n",
    "x1 = np.arange(1,3,0.1)\n",
    "y1 = squareTwo(x1)\n",
    "\n",
    "plt.plot(x, y, 'r--o')\n",
    "plt.plot(x, x, 'k-')\n",
    "plt.plot(x1, y1, 'b-')\n",
    "plt.xlabel(\"x\", fontsize = 22)\n",
    "plt.text(3, 1, r\"$x_n = 1-\\frac {(x_{n-1})^2} {2} +(x_{n-1}) $\", fontsize = 22, color = 'b')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### 不动点迭代格式2"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 19,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "1 \t\t 1.3333333333333333 \t\t -0.6666666666666667\n",
      "2 \t\t 1.4074074074074074 \t\t 0.07407407407407418\n",
      "3 \t\t 1.4138088705989937 \t\t 0.0064014631915862985\n",
      "4 \t\t 1.4141903630708597 \t\t 0.0003814924718659185\n",
      "5 \t\t 1.414212235403363 \t\t 2.1872332503392045e-05\n",
      "6 \t\t 1.4142134864818372 \t\t 1.2510784741515124e-06\n",
      "7 \t\t 1.4142135580327992 \t\t 7.155096204414235e-08\n",
      "8 \t\t 1.414213562124869 \t\t 4.092069794126019e-09\n",
      "9 \t\t 1.4142135623588987 \t\t 2.340296845204648e-10\n",
      "10 \t\t 1.4142135623722831 \t\t 1.3384404695671037e-11\n",
      "11 \t\t 1.4142135623730483 \t\t 7.651657085716579e-13\n",
      "12 \t\t 1.4142135623730923 \t\t 4.39648317751562e-14\n",
      "13 \t\t 1.414213562373095 \t\t 2.6645352591003757e-15\n",
      "14 \t\t 1.414213562373095 \t\t 0.0\n",
      "15 \t\t 1.414213562373095 \t\t 0.0\n",
      "16 \t\t 1.414213562373095 \t\t 0.0\n",
      "17 \t\t 1.414213562373095 \t\t 0.0\n",
      "18 \t\t 1.414213562373095 \t\t 0.0\n",
      "19 \t\t 1.414213562373095 \t\t 0.0\n",
      "20 \t\t 1.414213562373095 \t\t 0.0\n"
     ]
    },
    {
     "data": {
      "text/plain": [
       "Text(3, 1.4, '$x_n = x_{n-1}+\\\\frac {2} {3} +\\\\frac {(x_{n-1}^2)} {3} $')"
      ]
     },
     "execution_count": 19,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "import matplotlib.pyplot as plt\n",
    "import numpy as np\n",
    "%matplotlib inline\n",
    "def squareTwo(old):\n",
    "    return old+2/3-((old**2)/3)\n",
    "\n",
    "old = 2\n",
    "new = 0\n",
    "x = []\n",
    "y = []\n",
    "for val in range(20):\n",
    "    x.append(old)\n",
    "    new = squareTwo(old)\n",
    "    y.append(old)\n",
    "    x.append(old)\n",
    "    y.append(new)\n",
    "    \n",
    "    print(val + 1, \"\\t\\t\", new, \"\\t\\t\", new - old)\n",
    "    old = new\n",
    "x1 = np.arange(1,3,0.1)\n",
    "y1 = squareTwo(x1)\n",
    "\n",
    "plt.plot(x, y, 'r--o')\n",
    "plt.plot(x, x, 'k-')\n",
    "plt.plot(x1, y1, 'b-')\n",
    "plt.xlabel(\"x\", fontsize = 22)\n",
    "plt.text(3,1.4, r\"$x_n = x_{n-1}+\\frac {2} {3} +\\frac {(x_{n-1}^2)} {3} $\", fontsize = 22, color = 'b')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### 不动点迭代格式3"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 20,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "1 \t\t 2.4166666666666665 \t\t -0.5833333333333335\n",
      "2 \t\t 1.95156994673395 \t\t -0.4650967199327165\n",
      "3 \t\t 1.6375831471504458 \t\t -0.3139867995835042\n",
      "4 \t\t 1.4797602113237025 \t\t -0.15782293582674334\n",
      "5 \t\t 1.4280657455421544 \t\t -0.05169446578154813\n",
      "6 \t\t 1.4167110280097925 \t\t -0.011354717532361835\n",
      "7 \t\t 1.4146460196041568 \t\t -0.0020650084056357265\n",
      "8 \t\t 1.4142878792171418 \t\t -0.0003581403870149824\n",
      "9 \t\t 1.4142263166403541 \t\t -6.156257678768817e-05\n",
      "10 \t\t 1.4142157507628645 \t\t -1.0565877489598918e-05\n",
      "11 \t\t 1.4142139378444658 \t\t -1.8129183987358743e-06\n",
      "12 \t\t 1.4142136267938874 \t\t -3.1105057840541406e-07\n",
      "13 \t\t 1.4142135734259582 \t\t -5.336792918697597e-08\n",
      "14 \t\t 1.4142135642694666 \t\t -9.156491564965563e-09\n",
      "15 \t\t 1.414213562698461 \t\t -1.571005547873483e-09\n",
      "16 \t\t 1.4142135624289192 \t\t -2.6954194431993983e-10\n",
      "17 \t\t 1.4142135623826728 \t\t -4.6246340090760896e-11\n",
      "18 \t\t 1.4142135623747385 \t\t -7.934319867786144e-12\n",
      "19 \t\t 1.414213562373377 \t\t -1.361577517400292e-12\n",
      "20 \t\t 1.4142135623731433 \t\t -2.3359092438113294e-13\n"
     ]
    },
    {
     "data": {
      "text/plain": [
       "Text(5.1, 2.5, '$x_n =\\\\frac {(x_{n-1})^3 + 2}  {(x_{n-1})^2 + x_{n-1}} $')"
      ]
     },
     "execution_count": 20,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "import matplotlib.pyplot as plt\n",
    "import numpy as np\n",
    "%matplotlib inline\n",
    "def squareTwo(old):\n",
    "    return (old**3+2)/(old**2+old)\n",
    "\n",
    "old = 3\n",
    "new = 0\n",
    "x = []\n",
    "y = []\n",
    "for val in range(20):\n",
    "    x.append(old)\n",
    "    new = squareTwo(old)\n",
    "    y.append(old)\n",
    "    x.append(old)\n",
    "    y.append(new)\n",
    "    \n",
    "    print(val + 1, \"\\t\\t\", new, \"\\t\\t\", new - old)\n",
    "    old = new\n",
    "x1 = np.arange(1,5,0.1)\n",
    "y1 = squareTwo(x1)\n",
    "\n",
    "plt.plot(x, y, 'r--o')\n",
    "plt.plot(x, x, 'k-')\n",
    "plt.plot(x1, y1, 'b-')\n",
    "plt.xlabel(\"x\", fontsize = 22)\n",
    "plt.text(5.1, 2.5, r\"$x_n =\\frac {(x_{n-1})^3 + 2}  {(x_{n-1})^2 + x_{n-1}} $\", fontsize = 22, color = 'b')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### 不动点迭代格式4"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 21,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "1 \t\t -0.5 \t\t -3.5\n",
      "2 \t\t 0.375 \t\t 0.875\n",
      "3 \t\t 1.3046875 \t\t 0.9296875\n",
      "4 \t\t 1.453582763671875 \t\t 0.148895263671875\n",
      "5 \t\t 1.397131338249892 \t\t -0.056451425421983004\n",
      "6 \t\t 1.4211433500899249 \t\t 0.024012011840032876\n",
      "7 \t\t 1.4113191393375175 \t\t -0.009824210752407359\n",
      "8 \t\t 1.4154082828073218 \t\t 0.004089143469804268\n",
      "9 \t\t 1.413717979287536 \t\t -0.0016903035197857186\n",
      "10 \t\t 1.414418716807119 \t\t 0.0007007375195828836\n",
      "11 \t\t 1.4141285635799705 \t\t -0.0002901532271484264\n",
      "12 \t\t 1.4142487664135952 \t\t 0.00012020283362468298\n",
      "13 \t\t 1.4141989797624073 \t\t -4.978665118793302e-05\n",
      "14 \t\t 1.4142196025818905 \t\t 2.0622819483229193e-05\n",
      "15 \t\t 1.4142110604184503 \t\t -8.542163440150574e-06\n",
      "16 \t\t 1.4142145987135115 \t\t 3.538295061167318e-06\n",
      "17 \t\t 1.4142131331063024 \t\t -1.4656072091501215e-06\n",
      "18 \t\t 1.4142137401811303 \t\t 6.070748279629612e-07\n",
      "19 \t\t 1.4142134887225795 \t\t -2.514585508706091e-07\n",
      "20 \t\t 1.414213592880135 \t\t 1.0415755546944183e-07\n"
     ]
    },
    {
     "data": {
      "text/plain": [
       "Text(5.2, -2, '$x_n = 1 - \\\\frac {(x_{n-1})^2} {2} + x_{n-1} $')"
      ]
     },
     "execution_count": 21,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "import matplotlib.pyplot as plt\n",
    "import numpy as np\n",
    "%matplotlib inline\n",
    "def squareTwo(old):\n",
    "     return 1-((old**2)/2)+old\n",
    "\n",
    "old = 3\n",
    "new = 0\n",
    "x = []\n",
    "y = []\n",
    "for val in range(20):\n",
    "    x.append(old)\n",
    "    new = squareTwo(old)\n",
    "    y.append(old)\n",
    "    x.append(old)\n",
    "    y.append(new)\n",
    "    \n",
    "    print(val + 1, \"\\t\\t\", new, \"\\t\\t\", new - old)\n",
    "    old = new\n",
    "x1 = np.arange(1,5,0.1)\n",
    "y1 = squareTwo(x1)\n",
    "\n",
    "plt.plot(x, y, 'r--o')\n",
    "plt.plot(x, x, 'k-')\n",
    "plt.plot(x1, y1, 'b-')\n",
    "plt.xlabel(\"x\", fontsize = 22)\n",
    "plt.text(5.2, -2, r\"$x_n = 1 - \\frac {(x_{n-1})^2} {2} + x_{n-1} $\", fontsize = 22, color = 'b')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### 不动点迭代格式5"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 22,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "1 \t\t 2.4615384615384617 \t\t -0.5384615384615383\n",
      "2 \t\t 2.035186690251948 \t\t -0.4263517712865137\n",
      "3 \t\t 1.7367425402223466 \t\t -0.29844415002960134\n",
      "4 \t\t 1.5600918163960085 \t\t -0.17665072382633817\n",
      "5 \t\t 1.4732098857551736 \t\t -0.08688193064083483\n",
      "6 \t\t 1.4365252153189814 \t\t -0.03668467043619228\n",
      "7 \t\t 1.4223912468501965 \t\t -0.014133968468784897\n",
      "8 \t\t 1.417173296252181 \t\t -0.005217950598015442\n",
      "9 \t\t 1.4152797135152422 \t\t -0.001893582736938848\n",
      "10 \t\t 1.4145969463969574 \t\t -0.0006827671182847439\n",
      "11 \t\t 1.4143513397417526 \t\t -0.00024560665520478864\n",
      "12 \t\t 1.4142630645236363 \t\t -8.827521811638483e-05\n",
      "13 \t\t 1.4142313466054393 \t\t -3.171791819700509e-05\n",
      "14 \t\t 1.414219951382968 \t\t -1.1395222471177746e-05\n",
      "15 \t\t 1.414215857609693 \t\t -4.093773275037904e-06\n",
      "16 \t\t 1.4142143869282897 \t\t -1.4706814033260684e-06\n",
      "17 \t\t 1.4142138585910768 \t\t -5.283372128683794e-07\n",
      "18 \t\t 1.4142136687881062 \t\t -1.8980297067372476e-07\n",
      "19 \t\t 1.4142136006022146 \t\t -6.818589159962585e-08\n",
      "20 \t\t 1.4142135761067351 \t\t -2.4495479422625976e-08\n"
     ]
    },
    {
     "data": {
      "text/plain": [
       "Text(4.5, 2.5, '$x_n = 1-\\\\frac {(x_{n-1})^2} {2} +(x_{n-1}) $')"
      ]
     },
     "execution_count": 22,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "import matplotlib.pyplot as plt\n",
    "import numpy as np\n",
    "%matplotlib inline\n",
    "def squareTwo(old):\n",
    "    return (2+old**3+old)/(old**2+old+1)\n",
    "\n",
    "old = 3\n",
    "new = 0\n",
    "x = []\n",
    "y = []\n",
    "for val in range(20):\n",
    "    x.append(old)\n",
    "    new = squareTwo(old)\n",
    "    y.append(old)\n",
    "    x.append(old)\n",
    "    y.append(new)\n",
    "    \n",
    "    print(val + 1, \"\\t\\t\", new, \"\\t\\t\", new - old)\n",
    "    old = new\n",
    "x1 = np.arange(1,5,1)\n",
    "y1 = squareTwo(x1)\n",
    "\n",
    "plt.plot(x, y, 'r--o')\n",
    "plt.plot(x, x, 'k-')\n",
    "plt.plot(x1, y1, 'b-')\n",
    "plt.xlabel(\"x\", fontsize = 22)\n",
    "plt.text(4.5, 2.5, r\"$x_n = 1-\\frac {(x_{n-1})^2} {2} +(x_{n-1}) $\", fontsize = 22, color = 'b')"
   ]
  }
 ],
 "metadata": {
  "kernelspec": {
   "display_name": "Python 3",
   "language": "python",
   "name": "python3"
  },
  "language_info": {
   "codemirror_mode": {
    "name": "ipython",
    "version": 3
   },
   "file_extension": ".py",
   "mimetype": "text/x-python",
   "name": "python",
   "nbconvert_exporter": "python",
   "pygments_lexer": "ipython3",
   "version": "3.8.5"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 4
}
